U.S. Pat. No. 4,690,310 issued Sept. 1, 1987 to the same inventor and assigned to the same assignee as the present application, describes a sleeve pump specially designed to dispense fluids to within .+-.1% accuracy in metered amounts as small as 0.005 cc. Certain industrial applications would be enhanced by the accurate metered dispensation of fluids as described in the above referenced patent application into closely spaced vials or similar containers. A fluid dispensing apparatus that incorporated the ability to accurately dispense fluids in small metered amounts into a compact pump design applicable to a closely spaced multiple nozzle system would be a decided advantage in such applications.